📌 Key Points
- Perimeter is the total distance around boundary of a shape (linear units: cm, m).
- Area is the space enclosed inside a shape (square units: cm², m²).
- Same perimeter does NOT mean same area. Two different shapes can have equal perimeter but different areas.
- Rectangle: All angles are 90°, opposite sides are equal. Perimeter = 2(l+b), Area = l×b
- Square: Special rectangle where all sides are equal. Perimeter = 4a, Area = a²
- Triangle: Perimeter = sum of all sides. Area = (1/2) × base × height. Height must be perpendicular to base.
- Circle: All points equidistant from center. Circumference = 2πr = πd. Area = πr²
- Radius (r): Distance from center to any point on circle. Diameter (d) = 2r
- π (pi) ≈ 22/7 (for exact answers) or 3.14 (for approximations).
- Always check units in final answer. Perimeter has 1 unit, area has 2 units.
- For rectangles, write formulas carefully: 2(l+b) means 2 × (sum), not 2×l + b
- For triangles, height is the perpendicular distance from vertex to opposite side, not a slant side.
- For circles, use diameter (d) formula when diameter is given, use radius (r) when radius is given.
- Word problems often ask for both perimeter and area, or involve cost calculations based on these.
- Heron's formula for triangle area when sides are known: Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
📘 Important Definitions
🔢 Formulas & Laws
Perimeter of Rectangle
P = 2(l + b) or P = 2l + 2b
where l = length, b = breadth
Area of Rectangle
A = l × b
where l = length, b = breadth
Perimeter of Square
P = 4a
where a = side of square
Area of Square
A = a²
where a = side of square
Area of Triangle
A = (1/2) × b × h or A = (b × h)/2
where b = base, h = perpendicular height
Circumference of Circle
C = 2πr = πd
where r = radius, d = diameter, π ≈ 22/7 or 3.14
Area of Circle
A = πr²
where r = radius, π ≈ 22/7 or 3.14
Heron's Formula (Triangle)
A = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
Used when three sides of triangle are known
Relationship: Radius and Diameter
d = 2r or r = d/2
Diameter is twice the radius
⚠️ Common Mistakes
✗ Wrong: Using diameter in area formula: A = π(d)² instead of A = πr²
✓ Correct: Correct: Area of circle = πr², NOT π(d)². Convert diameter to radius first if needed.
✗ Wrong: Writing perimeter formula as 2l + b instead of 2(l + b) and calculating wrongly
✓ Correct: Correct: P = 2(l + b) = 2×l + 2×b. Both are same but 2(l+b) prevents errors.
✗ Wrong: Using slant side of triangle as height in area formula
✓ Correct: Correct: Height must be perpendicular to base, not a slant side. Draw ⊥ from vertex to base.
✗ Wrong: Confusing radius and diameter in circumference: Using radius formula for diameter given
✓ Correct: Correct: If diameter given, use C = πd. If radius given, use C = 2πr.
✗ Wrong: Forgetting units or writing wrong units (e.g., writing cm² for perimeter)
✓ Correct: Correct: Perimeter uses 1 unit (cm, m). Area uses 2 units (cm², m²).
✗ Wrong: Not converting units before calculating (e.g., mixing m and cm)
✓ Correct: Correct: Convert all measurements to same unit before calculating.
📝 Exam Focus
These questions are frequently asked in CBSE exams:
🎯 Last-Minute Recall
Close your eyes and try to recall: Key definitions, formulas, and 3 common mistakes. If you can recall 80% without looking, you're exam-ready!